Question

Network security:

1. If the prime numbers p and q are 5 and 13. Respectively, in the RSA technique, drive the public and private keys. Also show the encryption and decryption of a message m = 5.

2. Will the following work for an integrity check in electronic mail? When Alice sends a message to Bob, she computes a message digest of the message, and sends the message digest along with the message.

3. In the above scenario, is any extra security for integrity gained by having Alice encrypt the message digest with Bob’s public key? Why or why not?

Answer 1

a.

Given two primes p and q

p = 5 and q = 13

Let n = p x q = 5 x 13 = 65

Let z = (p-1) x (q-1) = (5 -1) x (13-1) = 4 x 12 = 48

We choose a number e , it should be less than z and should be relatively prime with n

Choose e = 7

Now choose a number d such that

ed mod z = 1

d = 7

So , the public key is (e,n) = (7,65) and the private key is (d,n) = (7,65)

Given that the message m = 5

Encryption : m^e mod n = 5⁷ mod 65 = 60

Decryption : c^d mod n = 60⁷ mod 65 = 5

b.

Yes the following will work for message integrity because if the message digest contains the hash of the message and if the message is tampered with, the hash value of the tampered message generated by Bob will not match the hash value sent by Alice.

c.

No extra security for the integrity is gained if Alice encrypts the message with Bob's public key because the integrity of a message depends only on its contents. Encrypting the message with Bob's public key doesn't add anything to the integrity of the message.